def stock_monte_carlo(start_price, days, mu, sigma):
'''
Function takes in stock price, number of days to run, mean and standard deviation values'''
# An emptry array
price = np.zeros(days)
# Initial Price
price[0] = start_price
# Shock and drift
shock = np.zeros(days)
drift = np.zeros(days)
# Formula: New price = Old price + Old price*(shock + drift)
for x in range(1,days):
shock[x] = np.random.normal(loc=mu*dt,scale=sigma*np.sqrt(dt))
drift[x] = mu * dt
price[x] = price[x-1] + (price[x-1] * (drift[x]+shock[x]))
return price
def Monte_Carlo_Analysis(Inp, mu, sigma, N=1e2, days = days):
# get the data for each symbol
df = Disp_Data(Inp)
# set the last entry of the open column as the starting price
start_price = df['Open'][-1]
# Ouput Figure
N = int(N)
fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize=(16, 8))
for run in range(100):
_ = plt.plot(stock_monte_carlo(start_price, days, mu, sigma))
_ = ax.set_xlabel('Days')
_ = ax.set_ylabel('Price')
_ = ax.set_title('Monte Carlo Analysis for %s' % Stock_Dic[Inp], weight='bold', fontsize = 16)
_ = ax.set_xlim([0,days])
return df
def Final_price_distribution_simulations(Inp, mu, sigma, N= 1e4, days = days):
# get the data for each symbol
df = Disp_Data(Inp)
# set the last entry of the open column as the starting price
start_price = df['Open'][-1]
# Simulations array
N = int(N)
simulations = np.zeros(N)
# Progress Bar
Counter = 0
Progress_Bar = progressbar.ProgressBar(maxval= N, widgets=[progressbar.Bar('#', '|', '|'), progressbar.Percentage()])
Progress_Bar.start()
for i in range(N):
simulations[i] = stock_monte_carlo(start_price, days, mu, sigma)[days-1]
Counter+=1
Progress_Bar.update(Counter)
Progress_Bar.finish()
return simulations
def Final_price_distribution_plot(simulations, Inp):
# get the data for Inp teach
df = Disp_Data(Inp)
# set the last entry of the open column as the starting price
start_price = df['Open'][-1]
# Output Figure
fig, ax = plt.subplots(nrows = 1, ncols = 1, figsize=(16, 8))
q = np.percentile(simulations, 1)
_ = ax.hist(simulations, bins='auto', color = '#34495e')
_ = plt.figtext(0.75, 0.80, "Start price: $%.2f" % start_price, fontsize = 12)
_ = plt.figtext(0.75, 0.75, "Mean final price: $%.2f" % simulations.mean(), fontsize = 12)
_ = plt.figtext(0.75, 0.70, "VaR(0.99): $%.2f" % (start_price -q,), fontsize = 12)
_ = plt.figtext(0.15,0.665, "q(0.99): $%.2f" % q, fontsize = 12)
_ = ax.set_xlim()
_ = ax.axvline(x=q, linewidth=4, color='#e74c3c')
_ = ax.set_title("Final price distribution for %s after %s days" % (Stock_Dic[Inp], days), weight='bold', fontsize = 16)
